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3. Determine the set of points at which the function f(x,y) = is continuous. (4 P.
3. Determine the set of points at which the function 2,,2 if (, y r,y)- S continuous. if (x, y)- (0, 0 3. Determine the set of points at which the function 2,,2 if (, y r,y)- S continuous. if (x, y)- (0, 0
Determine the set of points at which the function is continuous. f(x, y, z) = 7x + 2y + z D = = x, y, z) | 2 24v 7x + 2y } * Need Help? Read It Talk to a Tutor
4. Find k for which the function given by f(x, y) = P(X = x, Y = y) = kxy, for x = 1, 2, 3; y = 1,2,3, can serve as a joint probability distribution. [2 points) Also, determine the following: • F(2, 2). [2 points) • the marginal distribution of X; [2 points) • the marginal distribution of Y; [2 points] • P(X > 1, Y < 3). (2 points] • P(X = 1, Y <3). [2 points)
Please solve the 3 questions. Question 1: Determine the set of the points at which each given function is continuous: 1) f(x,y) = (5 Marks 4-x2 - y2 (2) g(x,y,z) = In x2 + y2 - 61 Cosz (x2 - y2 + z) 3) h(x,y,z) = x + 2y - 2 x2 + y2 1
arbitrary continuous function f(x, y, z) in spherical coordinates over the solid shown Set up the triple integral of an (Assume a 1 and b = 3.) f(x, у, z) dv = Ju/2 C фр Өр др arbitrary continuous function f(x, y, z) in spherical coordinates over the solid shown Set up the triple integral of an (Assume a 1 and b = 3.) f(x, у, z) dv = Ju/2 C фр Өр др
1. Determine the set of points at which the function (r,y) = cos V1 -2- y2 is continuous. Sketch the region.
consider continuous joint density function f(x,y)= (x+y)/7; 1<x<2, 1<y<3 Marginal density for Y? Select one: (2+3x)/14 (3+2y)/7 (2+3y)/14 (3+2y)/14 consider continuous joint density function f(x,y)= (x+y)/7 ; 1<x<2, 1<y<3 P(0<x<3, 0<y<4)=? Select one: 0.5 1 0.15 0.25
Set up the triple integral of an arbitrary continuous function f(x, y, z) in cylindrical or spherical coordinates over each solid shown & described below. i.e., Fill in the six limits of integration and the blank at the end. There is nothing to evaluate. (a) The solid is between the top hemisphere of the ball of radius 2 centered at the origin and the inside of the upper half cone z = Vx2 + y2. r?+ y2 + = 4...
Question 3 Let the function f be defined by f(x,y)--3y3 +4y2-15y +x2-8x. The set A consists of all points (x,y) in the xy-plane that satisfy 0sx S 10, 0sy s10 and x +y28.Find the global minimum value of f(x,y) over the set A. (Hint: see example 8 in lecture 7.) (6 marks) Question 3 Let the function f be defined by f(x,y)--3y3 +4y2-15y +x2-8x. The set A consists of all points (x,y) in the xy-plane that satisfy 0sx S 10,...
Determine the value of such that the function f (x, y) = cxy for 0<x<3 and 0 <y<3 satisfies the properties of a joint probability density function. Determine the following. Round your answers to four decimal places (e.g. 98.7654). 1.0994 P&<2,Y<3) 7.4444 P(X<2.0) 21:1878 Pu<Y<1,7) 12489 P(X>1.8,1 <Y<2.5) 7:3733 EX) P(X < 0,8< 4)